Find a three-digit number that, when divided by 4 and 15, gives equal non-zero residuals.

To solve this problem, you must first find the least common multiple. To do this, it is necessary to factor the number 15 and the number 4 into factors starting with the smallest, namely 15 = 3 x 5 and 4 = 2 x 2. Since the factors of both numbers do not coincide, then to find the smallest common multiple, all these numbers must be multiplied, namely: LCM = 3 x 5 x 2 x 2 = 60. But the problem is the question of finding a 3-digit number. Therefore, you need to find a 3-digit number that, when divided by the LCM, will give the whole remainder. The closest such number (or the smallest common multiple of a three-digit number for 60) will be 120. Dividing 120 by 15 and 4 will be 8 and 30, respectively.